# The Shape of Spacetime.

We have a theory of grand unification.

We don't. We have several candidate theories, of which the simplest ones are known
false (proton decay). Also even in situations where we do have good theories for the underlying physics getting from that to observable predictions can be quite painful. No one has been able to calculate the proton mass for examplpe.

Had inflation occured within what is describable that way, we'd already have a theory of inflation.We are if we ask, will the inflation be eternal or not?

We can't go from QCD -> mass of proton yet.

If you think that is not true, give me one experiment that has been done or could be done with current technology that definitiverly comes out A if inflation is eternal, and not A if it isn't.

The Guth paper points out that observation of curvature would rule out some models of eternal inflation.

What I said is unknowable is that is going on in domains that we cannot observe.

It's possible to make strong inferences about things that you can't directly observe. For example, we can't observe the core of the earth directly, but that doesn't prevent us from saying meaningful things about it.

We already can make statements about parts of the universe outside of the observation radius.

Which will again be a model, just like the current flat model is, and it will again not really tell us what is going on in the regions we cannot observe, just as the current model cannot.

If you keep insisting that the current cosmological model requires that the universe be flat, then this conversation is going to go nowhere. I'm about to give up here.

If we detect some miniscule curvature in the observable universe, why on Earth would we extrapolate that, as we would need to, to a volume hundreds or thousands of times larger than what we can observe?

Because we can tell from observational data how much the universe inflated, and then this gives you the radius at which you can extrapolate local observations.

Also, a lot of scientific statements are of the form, if X then Y. If you argue that curvature can't be extrapolated, then you *must* believe that the universe is non-isotropic. You can then look for signs of non-isotropy.

Calculate the precision in the curvature you would need at the end of inflation to produce a flatness that was within, say, 0.1% of 1 today.

It's on the order of 10^-18. That's not zero.

The mass of the electron is 10^-31 kg. That's not also zero.

Also, the amount of curvature that you would need to produce a flatness that is within a factor of 100 of 1 is 10^-14. If you have any flatness that is within a factor of a million of 1, you are going to have something to explain.

That is the whole reason for the invention of anthropic thinking, to be able to have a straight face as we say that the numbers are unexpected by 100 orders of magnitude.

You are missing the point. The reason inflation is cool is that it *avoids* the need for anthropic thinking. Without inflation, you have to have this weird coincidence to have any sort of curvature that is within a factor of a million of what we observe. With inflation, you don't.

You mean the papers that refer to eternal inflation? They just make my point-- they are based in anthropic thinking, which is required to get nonflat universes from inflation.

No they don't. If you want, you can just say that the universe works that way. Also since the inflation mechanism is unknown, the statement that anthropic thinking is required to get non-flat universes is something without any basis.

Sure you can get it published, but it is very far from mainstream astronomy, and I personally know few astronomers who would ever teach anthropic models of the universe to a class

I know the cosmologist that published the paper that made anthropic models respectable. He has a Nobel prize in physics, and I presume he teaches the topic in his class in cosmology.

At this point, I don't think it's possible to have a decent class in cosmology without mentioning the anthropic principle. I'm personally skeptical of anthropic arguments, but it's an idea with enough backing that you can't avoid teaching it.

I've told you why I reject that as mainstream science, as does almost every astronomer I know (I know a lot, outside the subfield of speculative cosmology).

I don't *like* the anthropic principle, but it's certainly not "outside the bounds of mainstream science."

do you still hold to your claim in the absence of anthropic thinking, i.e., in a model where you just get one universe, not 10100 to pick from to get the result you want?

Without inflation, you either have to chose fine-tuning or anthropic arguments to get any flatness < million. With inflation, you don't have to fine tune or use anthropic arguments to get that result. That's good.

Your statement would only have been true had we been able to observe the whole universe, which we already know we cannot do. You apparently think that if we observe a tiny curvature, it means the whole universe, beyond what we can observe, will match that same curvature.

No I don't. If we observe a tiny curvature, and the universe is isotropic and homogenity, then everything will match that curvature. We then look observational results which measure isotropy and homogenity to see what the limits on that are.

If it turns out that the universe is finite, then we could using observations to establish that the universe is isotropic within the radius of curvature of the universe.

Correction-- whether the observable universe is curved or flat is purely an observational issue! We already know what the whole universe is doing is not an observable issue, that's the point.

Not true. If the universe is finite then we can measure the entire universe. If it isn't then we can't. We don't know whether the universe is finite or not.

What's more, the current evidence is that it is flat, a point that you seemed to dispute earlier.

And I dispute it now. The current evidence is that the universe is within 0.01 of being flat. That's different from saying that it's flat. Also, there are some assumptions in the evidence that may not be true. The calculations assume GR is correct and that dark energy is the cosmological constant. If those are false, then the numbers could change.

As of 1995, the best numbers were that the universe had a curvature of -0.7. If it turns out that we aren't seeing dark energy, then we go back to those numbers.

Whether or not it could be curved, and inflation still be a good model, seems to be a matter of whether or not one views anthropic thinking as valid scientific reasoning.

You are changing your assertions. That's not necessarily a bad thing, but it will save me some effort if you now admit that non-zero curvature does not exclude inflation.

If you concede this point, then I don't see why raise anthropic principles. Guth only does so in his paper to reduce the search space of possible parameters.

Personally, I strongly dislike anthropic arguments. So lets reject the anthropic principle, and let's suppose we observe a positive curvature, I don't see the impact on inflation. There's enough evidence for inflation in the form of CMB background that I don't see what the issue is.

Ken G
Gold Member
Since inflation occurs at energies associated with the nuclear force, you can reasonably assume that quantum field theory still works. You then can assume a mathematical form for the potential that triggers inflation, and then see what happens.
So quantum field theory is now a theory of gravity? Does quantum field theory involve scalar gravitational potentials anywhere? We have laboratory evidence of such scalar potentials, which form part of the experimental basis of quantum field theory?

In the case of inflation, it turns out that a lot of the predictions are independent of the details.
Yes, that's what I meant by "standard inflation." But the key question all along here has been, should we count "eternal inflation", and the "multiverse", as "predictions that are independent of the details."? I certainly don't think so.
We aren't in the quantum gravity era in which we are doing total guess work. Inflation occurs at energies at which quantum field theory and general relativity are usable, and so you can make predictions based on QFT and GR. Where you don't know, you can put in an unknown variable.
But it's that "unknown variable" that is exactly the point. We do throw in a cosmological constant into GR, but only because there is an inescapable experimental need for it, and it causes a great deal of controversy. Models of inflation are nowhere near the kind of observational support of LCDM, and even given that, the recent Nobel prizes are viewed by many to be rather premature. I've never seen anything like a mainstream consensus about the proper details of a working inflation theory, but perhaps now the distinctions we are drawing are becoming somewhat subjective.

There is a *lot* less mumbo-jumbo in inflation than one might think. It's important not to confuse inflation with quantum gravity.
All right, I can grant that point, but it's not clear if that is saying something all that great about inflation models-- or something bad about loop quantum gravity!

Multiverses are quite different from eternal inflation.
Not in regard to the salient issue in this thread, which is, do we think that inflation leads to unmeasurable curvature without invoking some kind of multiverse/eternal inflation to allow us to view our theory as generic rather than incredibly finely tuned. I agree that if one does like to think anthropically, one can view inflation as a credible way to get some tiny but measurable curvature, but if one rejects that thinking as a way to validate a theory, then the detection of curvature would require looking for other theories than inflation.
You are wrong. Flatness is not generally assumed in LCDM. (There is one situation where people will assume flatness, and that's when trying to figure out the equation of state of the cosmological constant from observations and that's because you can't tell if the results are due to EOS or to curvature.)
I know it is not assumed in LCDM, that's the point-- it is a conclusion of LCDM. To wit, it is a conclusion that we successfully model the history of the universe by adopting a flat model, and furthermore, we have no reason to adopt any other model (by Occam's razor), and finally, if inflation is to be viewed as a good model (and anthropic arguments viewed as unscientific), then this will always be true. That doesn't mean we can't detect curvature, it means that if we do, we are going to start looking for alternatives to inflation the very next day, because embracing questionable anthropic arguments is going to feel like a real band-aid for inflation.
You are trying to teach cosmology (incorrectly) to people that have more experience in the topic than you do.
I'm not teaching cosmology, I'm pointing out the difference between a model, and a claim on the truth about the universe. Look at the title of the thread-- "the shape of spacetime" is a description of a mathematical model. That model exists, it is called LCDM. It is a flat model, because it is consistent with flatness, and models are always as simple as they can be yet still fit the data. It is not a claim on what we cannot observe, and never will observe. These are all just facts.
The two simple points are:

1) the current model of cosmology does not **assume** flatness
I never said it did. This is a result of model-making-- we use a flat model because we can, that's what makes it our best model. My entire point is that this does not make claims about the universe beyond what we can see, and what's more, we already know we cannot make claims about that, expressly because we know we will not be able to see it. We can weave a nice tale using eternal inflation and anthropic thinking, but every culture in history has weaved a nice creation myth-- that sure doesn't make it science. Empirical tests, not satisfying stories, is what makes something science.
2) inflation does not require undetectable curvature
Detectable curvature makes inflation a far weaker theory, it forces you to invoke anthropic thinking. I think that would motivate alternatives almost immediately, should curvature ever be detected, which seems unlikely. People also look for net rotation of the universe, there's no harm in looking.

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So quantum field theory is now a theory of gravity? Does quantum field theory involve scalar gravitational potentials anywhere? We have laboratory evidence of such scalar potentials, which form part of the experimental basis of quantum field theory?

In the inflationary era, the energies are low enough so that you can handle QFT and GR separately. In that situation, any scalar potentials from QFT just act as classical potentials. Also any spin-0 particle can be represented as a scalar field. You can do QFT with spin-0 nuclei and the math works out.

Also we do have cosmological evidence of a scalar potential. Dark energy.

Yes, that's what I meant by "standard inflation." But the key question all along here has been, should we count "eternal inflation", and the "multiverse", as "predictions that are independent of the details."?

You keep changing the key question. "Multiverses" don't have much to do with inflation. "Eternal inflation" is merely one scenario among half a dozen other inflationary scenarios, and I don't quite see it the point of focusing on that particularly one.

But it's that "unknown variable" that is exactly the point. We do throw in a cosmological constant into GR, but only because there is an inescapable experimental need for it, and it causes a great deal of controversy.

And we throw in curvature for the same reason.

[QUOTE Models of inflation are nowhere near the kind of observational support of LCDM, and even given that, the recent Nobel prizes are viewed by many to be rather premature. I've never seen anything like a mainstream consensus about the proper details of a working inflation theory[/QUOTE]

This is false. There are some very strong constraints on what you need in an inflationary theory.

Not in regard to the salient issue in this thread, which is, do we think that inflation leads to unmeasurable curvature without invoking some kind of multiverse/eternal inflation to allow us to view our theory as generic rather than incredibly finely tuned.

I don't see why this is a relevant question. The problem is that if you have any flatness coefficient that's less than a million, you are going to run into the same problem, and it doesn't matter whether its 0, 0.01, or 1000.

I know it is not assumed in LCDM, that's the point-- it is a conclusion of LCDM. To wit, it is a conclusion that we successfully model the history of the universe by adopting a flat model, and furthermore, we have no reason to adopt any other model (by Occam's razor)

This is false.

1) The data says that the universe is within 1% of flat. That's not flat.

2) Assuming flatness doesn't simplify the model. Even if the *average* curvature of the universe is zero, LCDM calculates the "variation" of curvature. So you are going to have to include spatial curvature no matter what you do.

3) LCDM contains some assumptions which are not completely firm. In particular it makes assumptions about dark energy, and if those are false, then we go back to curvature = -0.7.

4) You are entitled to your personal opinions, but the views that you are putting forth are not scientific consensus

Finally, if inflation is to be viewed as a good model (and anthropic arguments viewed as unscientific), then this will always be true.

You keep asserting this and it's false. Aside from the solving the flatness and horizon problems, inflation gives us a good mechanism to seed the initial density perturbations that are needed to model CMB.

That doesn't mean we can't detect curvature, it means that if we do, we are going to start looking for alternatives to inflation the very next day, because embracing questionable anthropic arguments is going to feel like a real band-aid for inflation.

This is false, and it's provably false.

Before the discovery of dark energy in 1998, the curvature of the universe was believed to be -0.7, but inflation was taught as part of standard cosmology. If we do find curvature, it's going to impact which inflation models are viable, but it's not going to kill the inflation mechanism.

Look at the title of the thread-- "the shape of spacetime" is a description of a mathematical model.

No its not. It's an observational reality.

That model exists, it is called LCDM. It is a flat model, because it is consistent with flatness, and models are always as simple as they can be yet still fit the data.

We are going in circles.

Here is LCDM

http://map.gsfc.nasa.gov/resources/camb_tool/index.html

You can change the knobs to get all sorts of curvatures.

My entire point is that this does not make claims about the universe beyond what we can see, and what's more, we already know we cannot make claims about that, expressly because we know we will not be able to see it.

Yes it does make claims. Those claims may be incorrect, but making incorrect claims is a good thing. LCDM does indeed make claims about the unobservable universe. Those may be incorrect, but that's an observational issue.

Detectable curvature makes inflation a far weaker theory, it forces you to invoke anthropic thinking.

No it doesn't. Also inflation reduces the need for anthropic thinking. Within inflation you don't have to fine tuning your initial conditions as much.

Also you can also get away from anthropic thinking by invoking fine tuning.

People also look for net rotation of the universe, there's no harm in looking.

Sure.....

http://arxiv.org/abs/astro-ph/0008106

Ken G
Gold Member
We don't. We have several candidate theories, of which the simplest ones are known
But then you are saying that inflation does not represent unknown physics, because it's just QFT and GR at the grand unification scale, but that also we don't have a theory at the grand unification scale! You are contradicting your own argument.
The Guth paper points out that observation of curvature would rule out some models of eternal inflation.
Yes, and note that just means that even with anthropic thinking inflation models do not necessarily survive the detection of curvature. That only strengthens what I'm saying, if you have to invoke eternal inflation and it still doesn't necessarily help.
We already can make statements about parts of the universe outside of the observation radius.
I am definining the "observable universe" to be whatever we have direct observational constraints on. When we look for curvature, what we see has some kind of physical radius associated with it, that includes the full sequence of inferences involved. We already know that will never be large enough to describe a closed universe, which is my point.
If you keep insisting that the current cosmological model requires that the universe be flat, then this conversation is going to go nowhere.
Where on Earth did you get the idea this conversation has had anything whatever to do with that claim? Have you been reading my words? I don't think that at all, and indeed argued strenuously against that the entire time. I think your frustration is coming from not listening.
If you argue that curvature can't be extrapolated, then you *must* believe that the universe is non-isotropic. You can then look for signs of non-isotropy.
You are missing the actual alternative there-- you just can't tell if it is isotropic or not, if all you detect is some teeny average curvature, and you simply accept that you won't get to tell, because you won't. You certainly don't have to believe it is non-isotropic, that is simply incorrect logic.
It's on the order of 10^-18. That's not zero.
Thank you for the number, that's helpful. Yes I know it's not zero, obviously, that's why I asked for it. The point is, you would find yourself in a position that you are advocating a theory that includes a parameter that must be specified to that degree of precision, based on observations with a precision that is probably 14 orders of magnitude less than that, and even GR itself is not established to that level of precision. That is a horrendous state of affairs, for a predictive theory to claim, there really would be nothing left of inflation if it had to be that precise of a theory to mean anything. It's what requires anthropic thinking to even suggest it with a straight face.
Also, the amount of curvature that you would need to produce a flatness that is within a factor of 100 of 1 is 10^-14. If you have any flatness that is within a factor of a million of 1, you are going to have something to explain.
Hence inflation, yes. Inflation is our explanation of flatness, and as such, it makes for a lousy explanation for very-near-but-measurably-not-flatness. A lousy explanation, that is, without anthropic thinking.
You are missing the point. The reason inflation is cool is that it *avoids* the need for anthropic thinking.
Only if the universe is not measurably curved, that is the whole point. That's also what Guth is saying-- as soon as you allow a detection of curvature, you are immediately thrust into an eternal inflation scenario, which is anthropic thinking-- we get to select the special inflation event that allowed us to be here, out of a vast number that have to actually occur.
Without inflation, you have to have this weird coincidence to have any sort of curvature that is within a factor of a million of what we observe. With inflation, you don't.
Obviously, that is quite central to my entire point. But the price you pay is that you succeed too well, if you ever detect any curvature. Immediately you are up to your neck in the anthropic escape hatch.
No they don't. If you want, you can just say that the universe works that way.
No, because that is the kind of statement you make about a measurement, not about a theory. You have to justify a theory, you don't get to say "the universe works that way", unless you are a witch doctor. You don't have to justify an observation, for that you can say "that's just how it is". How it works is an entirely different kettle of fish, that has to have some simplfying quality.

I know the cosmologist that published the paper that made anthropic models respectable. He has a Nobel prize in physics, and I presume he teaches the topic in his class in cosmology.
Not terribly surprising, is it, that a multiverse enthusiast would find multiverse arguments convincing? Do you think it's hard to find examples of highly decorated physicists who have non-mainstream ideas about cosmology that they might teach in their classes? What do you think Hannes Alfven taught, or Geoffrey Burbidge, or Hoyle? Speculation is fine in science, but calling it sound physics is another matter. What is viewed as "respectable" is largely political, it is what is viewed as mainstream that matters most.
At this point, I don't think it's possible to have a decent class in cosmology without mentioning the anthropic principle. I'm personally skeptical of anthropic arguments, but it's an idea with enough backing that you can't avoid teaching it.
You can "teach the controversy", if you like, but any self-respecting scientist who does that is going to be very clear that they have left the building of mainstream or empirically supported science. They are going to start feeling like a witch doctor if they say "here is what astronomers have accepted as the truth of our universe."
I don't *like* the anthropic principle, but it's certainly not "outside the bounds of mainstream science."
Yes it is, the way we use the term here (the strong version). The weak version is just a statement of fact, but the idea that our universe is selected out of many and this allows us to feel happy about highly fine-tuned theories is nothing short of a cop out. Science is about explaining what we observe by testing our hypotheses, not feeling good about what we observe by invoking things we cannot, or claiming that parameters that have values that we already know they must have is somehow a prediction of anthropic thinking. I don't think working astronomers are at all happy about anthropic thinking, it's largely a playground of people who go to meeting with other anthropic-thinkers. It is a very long way from catching on in the mainstream.
Without inflation, you either have to chose fine-tuning or anthropic arguments to get any flatness < million. With inflation, you don't have to fine tune or use anthropic arguments to get that result. That's good.
Except once again your statement only works if no curvature is detected, and is in exact agreement with everything I've said about inflation and curvature.
You are changing your assertions.
Not actually, because I have always rejected anthropic thinking as an allowable justification for a scientific theory. When you do that, all my previous statements are perfectly consistent with what I'm saying now. I'm just clarifying this better now.
That's not necessarily a bad thing, but it will save me some effort if you now admit that non-zero curvature does not exclude inflation.
It has always been obvious in this discussion that any inflation theory could precisely choose its parameters to get any curvature today. That's the meaning of a monotonic function, is this not completely obvious? The actual context of the discussion is how one of the main reasons for the inflation model, to remove the absurd fine-tuning of the curvature in the initial conditions, would be lost if inflation had to produce a similarly absurd fine tuning (I believe you quoted the number 10-18) if the post-inflation curvature had to increase to a tiny level we could observe today but haven't yet, like the 10-4 number quoted in that Guth article. That's exactly why anthropic thinking, in the form of eternal inflation, would need to return in that eventuality, which is my whole point.
Personally, I strongly dislike anthropic arguments. So lets reject the anthropic principle, and let's suppose we observe a positive curvature, I don't see the impact on inflation. There's enough evidence for inflation in the form of CMB background that I don't see what the issue is.
Well I'm glad we can agree to reject anthropic thinking, but if we observe positive curvature, calculate the post-inflation curvature that would be needed to explain that. How is that so different from the very anthropic thinking that would be needed to explain a universe with no inflation at all?

Just as an outsider reading this whole twofish-Ken G debate going on, I'll have two comments to make:

1) It has been very entertaining and as an undergraduate I have learned a lot from looking up a paper on a topic I did not know about when it was mentioned.

2) Twofish looks like he has a better understanding of all of the topics, and I think I found a contradiction or two in Ken G's arguments.

Keep going! I'm learning a lot. :D

But then you are saying that inflation does not represent unknown physics, because it's just QFT and GR at the grand unification scale, but that also we don't have a theory at the grand unification scale!

There are different levels of "known-ness." Our best guess right now is that GUT physics is such that both QFT and GR are valid, and there is no need to invoke weird quantum gravity. The form of the Langrangian at GUT energies is unknown, but you can put in different equations and see what happens.

When we look for curvature, what we see has some kind of physical radius associated with it, that includes the full sequence of inferences involved. We already know that will never be large enough to describe a closed universe

We don't know this. It's perfectly possible that we will observe a small but finite radius of curvature and use CMB spectrum to establish isotropy within the radius of curvature.

You just can't tell if it is isotropic or not, if all you detect is some teeny average curvature, and you simply accept that you won't get to tell, because you won't.

You can look for anisotropy within CMB and use that to constrain the radius in which we expect the universe to be isotropic.

The point is, you would find yourself in a position that you are advocating a theory that includes a parameter that must be specified to that degree of precision, based on observations with a precision that is probably 14 orders of magnitude less than that, and even GR itself is not established to that level of precision.

Which means that you can't use nucleosynthesis calculations to constrain flatness, but you can use local observations to do it. What happens is that whatever the value of flatness is at the end of inflation, it gets multipled by 16 orders of magnitude to the point that it may well be detectable if you use late universe observations.

Obviously, that is quite central to my entire point. But the price you pay is that you succeed too well, if you ever detect any curvature. Immediately you are up to your neck in the anthropic escape hatch.

No you aren't. If you detect curvature, then you look for the energy scale at which the inflation ends. At if it matches any sort of physical constant, then you have nothing to explain. The reason that inflation gets rid of anthropic and fine tuning is that anything that needs to get explained gets put into the somewhat unknown but not unknownable physics of inflation.

The actual context of the discussion is how one of the main reasons for the inflation model, to remove the absurd fine-tuning of the curvature in the initial conditions, would be lost if inflation had to produce a similarly absurd fine tuning (I believe you quoted the number 10-18) if the post-inflation curvature had to increase to a tiny level we could observe today but haven't yet, like the 10-4 number quoted in that Guth article. That's exactly why anthropic thinking, in the form of eternal inflation, would need to return in that eventuality, which is my whole point.

And that point is wrong.

The point of inflation is that you now have the ability to create a way of producing small but not zero curvatures *naturally*. For example, under some models of inflation, the universe expands until the curvature is small enough to allow quantum mechanical tunneling. What would happen in this situation is that the universe would expand until the curvature gets very small, particles tunnel out, and inflation ends, giving you a tiny curvature that blows up to a small one.

http://ned.ipac.caltech.edu/level5/Albrecht/Alb3_3.html

That might not work, but the point is that the thing about inflation is that it provides an alternative to anthropic and fine-tuning arguments. We'll only have to go back to anthropic and fine-tuning arguments once we run out of scenarios for inflation.

Well I'm glad we can agree to reject anthropic thinking

I didn't say that I reject. I said I don't like it. I'll accept it only when there are no alternatives. The point of inflation is that it gives you alternatives.

but if we observe positive curvature, calculate the post-inflation curvature that would be needed to explain that.

And if it turns out to be comparable to some subatomic scale, we have nothing to explain.

How is that so different from the very anthropic thinking that would be needed to explain a universe with no inflation at all?

Because you have unknown but not unknowable physics that you can look at before giving up.

It's pretty simple. If I flip a coin 50 times, and it all comes up heads, then I don't assume that God did this. I don't assume that there are a billion other coin flippers. My first assumption is that the coin is somehow rigged to always come up heads.

It's only after that I convince myself that the coin isn't rigged that I end up with headaches.

The thing about inflation is that it provides enough unknown physics so that you can argue that somewhere in there, the coin is rigged. If it turns out that the universe ends inflation with whatever curvature, then we look at the details of inflation to come up with reasons why the coin was rigged to come up with that value. It's only after eliminating the possibility that the coin is rigged that you end up with a philosophical problem.

If you go (initial conditions)->(inflation)->(current universe), then you end up with a black box in which you can try to invent some physics that explains the current set of parameters. If you go (initial conditions)->(current universe), then you don't have a place to hide a rigged coin.

If you argue initial conditions, you are basically saying "God did it." Instead of saying "God did it" you can say "inflation did it" which is different because inflation is subject to scientific inquiry.

Ken G
Gold Member
2) Twofish looks like he has a better understanding of all of the topics, and I think I found a contradiction or two in Ken G's arguments.
You are more than welcome to state what you see as a contradiction, and then I can tell you if you have interpreted me correctly. Let me caution you against accepting twofish-quant's versions of what I'm saying, they are often not even close.

Ken G
Gold Member
We don't know this. It's perfectly possible that we will observe a small but finite radius of curvature and use CMB spectrum to establish isotropy within the radius of curvature.
Where did I ever say we couldn't?? Again you are putting words in my mouth and changing my argument. Of course we could observe that, we could observe anything that doesn't contradict what we've already seen. But so what? Are you going to claim that if we observe a piece of the universe that has a consistent and tiny curvature, that this implies something about the rest of the universe that we do not observe? By what form of logic would you ever be able to do that? If we can barely observe the small curvature, just how precisely do you think we can establish its consistency, and how accurately could we ever extrapolate that with confidence? No, you are confusing the model we would create to fit that data with an assertion about something that we simply would not know and would not have any good reason to think that we know. You are confusing what goes into a good model (which includes Occam's razor) with what goes into knowledge about the universe (which does not).
You can look for anisotropy within CMB and use that to constrain the radius in which we expect the universe to be isotropic.
No we certainly could not form any such scientifically justified expectation, any more than a person standing in a volcanic crater can expect the whole Earth to be concave. The cosmological principle is a simplifying principle used in good models, it is not a constraint on something we've never seen and never will see. Not if you are doing science instead of generating plausible belief systems.
No you aren't. If you detect curvature, then you look for the energy scale at which the inflation ends. At if it matches any sort of physical constant, then you have nothing to explain.
Sure you do, if you detect curvature today. You would then have to explain why the physical constant had just the value necessary to let inflation end at a time that would lead to some small but measurable curvature today! That's my point, such a detection would strip the inflation model of most of its primary purpose, which is to make our universe seem natural or plausible-- without anthropic reasoning.

Thank you for this interesting article, but I hardly see where it is backing your claims, indeed I see several points that are completely in concert with my current understanding, including:

"The upshot is that additional scalar fields abound, at least in the imaginations of particle theorists, and if anything the problem for cosmologists has been that there are too many different models. It is difficult to put forward any one of them as the most compelling. This situation has caused the world of cosmology to regard the inflaton'' in a phenomenological way, simply investigating the behaviors of different inflaton potentials, and leaving the question of foundations to a time when the particle physics situation becomes clearer. "

I interpret that as saying that inflation models are somewhat "swinging in the dark", lacking sufficient constraints from established physics to be able to judge their plausibility, just as I thought.

And:
" Fine tuning of potential parameters is generally required to produce sufficient inflation in slow roll models. Essentially all current models of inflation use the slow roll mechanism."

Which I interpret as flying completely in the face of your argument that the point of inflation is to remove the need for fine tuning! Admittedly the fine tuning is not as horrendous as it would be without inflation, which is its raison d'etre, but the article has said nothing about ending up with a measurably curved universe today, and that would exacerbate the fine tuning problem drastically.
And if it turns out to be comparable to some subatomic scale, we have nothing to explain.
Being comparable won't cut it, it has to be exactly the atomic scale. In fact, if it came out close, you would know the atomic scale much more precisely from the inflationary constraints than anything we could actually measure. But if we observe finite curvature, now you have to explain why that atomic scale is so finely tuned as to produce that. That's why finite curvature today would be bad news for inflation proponents, the plausiblity of their exercise would drastically diminish.
Because you have unknown but not unknowable physics that you can look at before giving up.
But you are just hoping, you can also buy a lottery ticket if you want to get rich. Yes, it may be the only means you have for getting rich, but that doesn't make it a good strategy for making a living.
If I flip a coin 50 times, and it all comes up heads, then I don't assume that God did this. I don't assume that there are a billion other coin flippers. My first assumption is that the coin is somehow rigged to always come up heads.
That's not a very good analogy though. A better one would be to generate sequences of numbers, have them all come out the same, and hope that this won't seem finely tuned if what they come out to is the decimal expansion of pi! And even if it did come out that way, you still couldn't explain why a parameter equal to the decimal expansion of pi would be precisely in the range of parameters that would end up with tiny but measurable curvature, that would still be a complete mystery, and a finely tuned one at that.
The thing about inflation is that it provides enough unknown physics so that you can argue that somewhere in there, the coin is rigged.
Exactly, you can get it to do whatever you like. Just like the article said, there are way too many possibilities. The problem is, they would all be finely tuned, and extremely so if you need the model to end up with finite measurable curvature today.

If you go (initial conditions)->(inflation)->(current universe), then you end up with a black box in which you can try to invent some physics that explains the current set of parameters. If you go (initial conditions)->(current universe), then you don't have a place to hide a rigged coin.
Sure you do, you put it in the physics of the initial conditions, like a brane collision or some such thing. The point is, whatever model you come up with is going to have some parameters in it, and even if those parameters come from some existing physics, it's still fine tuned if you need to get a finite measurable curvature today.

Are you going to claim that if we observe a piece of the universe that has a consistent and tiny curvature, that this implies something about the rest of the universe that we do not observe?

Yes. I claim this. If we observe a piece of the universe that has a consistent curvature then we can conclude that either the parts of the universe that we can't directly observe are different *or* that the universe as a whole has a certain shape.

No, you are confusing the model we would create to fit that data with an assertion about something that we simply would not know and would not have any good reason to think that we know.

We can narrow down the alternatives.

Sure you do, if you detect curvature today. You would then have to explain why the physical constant had just the value necessary to let inflation end at a time that would lead to some small but measurable curvature today!

Why? I would have no need to do that anymore than I need to explain why the mass of the electron is such that I get a nice cup of coffee, or why the boiling point of water happens to be what it is.

If I flip a coin 50 times in a row and I find it's all heads, I have something to explain. If I find that it happens to be a two headed coin, then there is nothing to explain. The universe is set up so that no matter what the initial conditions are, it ends up a certain way and there is no fine tuning or anthropic argument necessary.

I interpret that as saying that inflation models are somewhat "swinging in the dark", lacking sufficient constraints from established physics to be able to judge their plausibility, just as I thought.

Exactly,

Which is why:

1) we need more high precision cosmological and particle physics experiments

2) it's not the end of the world if we find out that the universe has a curvature. If that happens we take our hundred or so inflation models and cross out the one's that require zero curvature. If it happens that we don't find curvature, we take a red pen and cross out the ones that require non-zero curvature.

Which I interpret as flying completely in the face of your argument that the point of inflation is to remove the need for fine tuning!

Slow roll models require fine tuning. That's why people don't like slow roll models.

Being comparable won't cut it, it has to be exactly the atomic scale. In fact, if it came out close, you would know the atomic scale much more precisely from the inflationary constraints than anything we could actually measure.

Cool isn't it.

But if we observe finite curvature, now you have to explain why that atomic scale is so finely tuned as to produce that.

No you don't. If the magic number is 10^-32, then after X years, I'll see curvature of 0.01. If the magic number is 10^-50, then after X+epsilon years, I'll see a curvature of 0.01. Seeing a finite curvature is independent of the magic minimum number.

If the universe has curvature, then what will happen is that it will eventually take every value between 0 and infinity, or 0 and -1 (assuming no cosmological constant at which point curvature will reach a maximum).

So the reason the universe has the curvature that it has is we happen to be around in the time that it happens to have a the current value. If it is 0.01 today, it will be 0.02 in X billion years 0.3 after some more time, and eventually it's going to plop to some large value at which point dark energy takes over.

But you are just hoping, you can also buy a lottery ticket if you want to get rich.

No. I happen to dislike anthropic arguments, and I suggest that we first get rid of all of the non-anthropic possibilities before we even start to consider anthropic ones. As long as there are any plausible non-anthropic mechanisms to eliminate, I suggest we get rid of those before going anthropic.

And even if it did come out that way, you still couldn't explain why a parameter equal to the decimal expansion of pi would be precisely in the range of parameters that would end up with tiny but measurable curvature, that would still be a complete mystery.

If I take a pack of playing cards and deal them, and I have them all in order. That would be weird. However, if I just deal them and I get some random sequence, that wouldn't be. So I find out when inflation ends, and it's some random number. So what?

Sure you do, you put it in the physics of the initial conditions, like a brane collision or some such thing. The point is, whatever model you come up with is going to have some parameters in it, and even if those parameters come from some existing physics, it's still fine tuned if you need to get a finite measurable curvature today.

No it's not. If I have inflation and the cosmological constant isn't high, then at some point in the life of the universe someone *will* see a curvature of 0.001. Once you invoke inflation then most observers at within a finite universe will see a measurable curvature. Once I invoke inflation, I can change when "today" is. If the minimum curvature value was 10^-16, then "today" is X years post inflation. If it's 10^-13, then "today" is X - epsilion years. If it's 10^-30, then "today" is X + epsilon years.

As far as why I see a curvature of 0.001 rather than 0.002, that's like asking why I was born in the late-1960's rather than in the 1980's, there's nothing to explain. Once you have *any* positive curvature in the universe and you have low enough dark energy, then *someone* is going to see a curvature of 0.001, and it might as well be you.

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bapowell
I can't see how you can claim that without some physical basis for the cause of the inflation. If you simply assert that inflation occured early in our universe, that is a statement that has nothing to do with eternal inflation. If you want to support that statement with some kind of physical theory, then you need to be able to say what observational tests that theory has satisfied, and there is a very long and exhaustive process that goes into gaining confidence in any such attempt. That currently just does not exist, so for the mainstream, inflation is just a statement of a phenomenon, not a theory, and no claims can be made on how likely or often it "should" occur.
A couple points I'd like to make in response to this. You make the statement here, and elsewhere throughout this thread (and I'm paraphrasing) that inflation has no physical basis, is not a theory and just a phenomenon, is flaky, has not passed experimental muster, etc. I disagree with this stance. Firstly, I don't know what precisely you mean by phenomenon, but I suppose you mean that it is an idea or statement about the early universe -- that it underwent exponential expansion early on -- but that there is a lack of understanding for how this could happen and no observational evidence that currently helps shape an underlying theory. I would argue that both of these assertions lack merit.

First, there is a mechanism by which inflation can be achieved within GR, and so we already have more than a mere phenomenon. This mechanism does make use of hypothetical scalar fields, which you claim is ad hoc. (So, I must ask, are you equally skeptical of gauge theories and spontaneous symmetry breaking?) Keep in mind that the stress-energy that drives inflation need not be a fundamental scalar, it only needs to have an effective equation of state that satisfies $w < -1/3$. Yes, we don't know precisely what the source of this stress-energy is, but that does not demote inflation to a mere ad hoc phenomenon.

Second, I would argue that there is a wealth of data supporting an early inflationary epoch. You claimed earlier than inflation makes not testable predictions beyond that which it was constructed to explain. I'm not sure I agree; first, what would you say inflation was constructed to explain? Flatness? Lack of monopoles? Resolve the horizon problem? I suppose that question can only be answered by learning the intent of the scientists who built the theory. I would say that even if we claim these were the prescribed goals of the theory, the discovery that inflation could generate the seeds of large scale structure was certainly not apparent at its conception. This realization came later, and it constitutes a definitive prediction of the inflationary proposal. So, we have a hypothesis: that a period of exponential expansion took place in the early universe, driven by a source of stress-energy with the quantum numbers of the vacuum. There are observations that address the first part of the hypothesis -- the exponential expansion. These are flatness of the observable universe, smoothness of the CMB together with its anisotropy, lack of monopoles, the presence of superhorizon-scale correlations in the temperature and polarization anisotropies in the CMB, and some others. But there are also observations that address that latter part of the hypothesis -- that a source with the quantum numbers of the vacuum drove the expansion. Such a source can be effectively modeled as a scalar field. We know certain facts about this field: it must have a potential energy that both supports inflation and ends it. We know it must have a shape that supports a sufficient amount of inflation. In its simplest form consistent with these requirements, it also makes predictions: namely, that the density perturbations will be adiabatic, Gaussian, and nearly scale invariant.

Now, taking the above into consideration, I have a predictive framework that does indeed rely on one major assumption -- the existence of an effective field with the quantum numbers of the vacuum. We have good reason to suspect that such fields exist, if our studies of symmetry breaking and gauge theories have anything to say about it. And within the above framework, I can begin to constrain my scalar potential; without understanding how inflation arises from the SM or some extension of it, this is a purely phenomenological endeavor since it is solely driven by data. This is what I mean by phenomenological. And from this approach, I can discover, by observations of the observable universe alone, whether the potential that drove inflation in our Hubble patch is operative elsewhere in the universe. It doesn't matter that I don't know how exactly the inflaton arises from supergravity or some other theory. The data, together a suitable application of Occam's razor, are sufficient.

And I must caveat this discussion by saying that I am not a proponent of eternal inflation or of multiverse theories per se; I have no vested interest in their veracity. But I think it is too constrictive to maintain your tact that unless it is strictly observed that it has no place in science. Many things that belong in mainstream science have not been strictly observed but only inferred or implied by the strict consistency of theories that have been supported by other observations.

Ken G
Gold Member
First, there is a mechanism by which inflation can be achieved within GR, and so we already have more than a mere phenomenon.
I would say you can claim that when the mechanism works, when one mechanism emerges from all the possibilities because it is well constrained and absent of any difficulties.
This mechanism does make use of hypothetical scalar fields, which you claim is ad hoc. (So, I must ask, are you equally skeptical of gauge theories and spontaneous symmetry breaking?)
Gauge theories are a unifying way of thinking about a wide class of behavior, and spontaneous symmetry breaking likewise-- it is a unifying principle. These ideas employ scalar potentials for only one reason, AFAIK-- because it is the simplest way to do it. That's it, that's the reason-- not because there is a shred of evidence that approach should work. Now, of course we would always start with the simplest approach, that's looking for the keys under the streetlight first. But it's still no reason to expect it will work, or that it is the "right physics", until there is some much better reason to expect that, based on some success that simply has not yet appeared. The keys have not been found yet, so the search under the streetlight continues, until either the keys are found, or the search moves on to somewhere more difficult. That is how we look for keys, but we don't need to pretend it is some better guided process than that!

Keep in mind that the stress-energy that drives inflation need not be a fundamental scalar, it only needs to have an effective equation of state that satisfies $w < -1/3$. Yes, we don't know precisely what the source of this stress-energy is, but that does not demote inflation to a mere ad hoc phenomenon.
It's not important to me to be able to label inflation "ad hoc", I'm perfectly happy with "currently speculative details of how it works." I hope inflation works out simply, why wouldn't I. I'm just saying we should not kid ourselves that we have good reason to expect a scalar potential mechanism to turn out to be the correct description of the phenomenon of inflation.

Second, I would argue that there is a wealth of data supporting an early inflationary epoch.
Yes, that's the "phenomenon" we are talking about. The question is, what is a good model of whatever mechanism made that happen?
You claimed earlier than inflation makes not testable predictions beyond that which it was constructed to explain. I'm not sure I agree; first, what would you say inflation was constructed to explain? Flatness? Lack of monopoles? Resolve the horizon problem? I suppose that question can only be answered by learning the intent of the scientists who built the theory. I would say that even if we claim these were the prescribed goals of the theory, the discovery that inflation could generate the seeds of large scale structure was certainly not apparent at its conception.
I'm saying it is appropriate to separate the phenomenon of inflation, which is simply the statement that the universe expanded by the factor X at epoch Y, from any physical theories or mechanisms that can actually accomplish that. Once making that distinction, we can then look for what observations we have that support the phenomenon, and what observations support the mechanism. I don't think that distinction has been clearly made, because the list of successes you cite all sound to me like they stem from the phenomenon itself-- the mechanism is still not accomplishing any of these independent successes, all it is doing is the one thing it was built to do-- to give the phenomenon.

Such a mechanism is not unifying anything, it's not a principle, until it can point to its own successes related to the mechanism independent from the basic phenomenon it is built to produce. Things like reheating and so forth could be examples of the mechanism working, beyond just the phenomenon, but these are exactly the kinds of details that are still being thrashed out, and remain unclear as to whether or not they are going to work. That's the natural state of affairs when a theory is being built, we don't know if we have the right construction to get something that works, so it's fine to try-- but we needn't pretend that we know we have a good mechanism just because we know we have a good phenomenon. That's not bashing the noble effort to look under the streetlight, it's just being realistic about it. Maybe you're right that if I knew better all the things that scalar potentials are doing for us, I'd be more inclined to see that approach to inflation as a unifying principle. But it starts to sound a bit like string theory, which I am also assured is doing wonderful things for our understanding, except that it hasn't really delivered what it claimed it would.

So, we have a hypothesis: that a period of exponential expansion took place in the early universe, driven by a source of stress-energy with the quantum numbers of the vacuum.
That's two hypotheses, one the phenomenon and one the mechanism, and we must not conflate the successes of each. They are important to keep separate.

But there are also observations that address that latter part of the hypothesis -- that a source with the quantum numbers of the vacuum drove the expansion. Such a source can be effectively modeled as a scalar field. We know certain facts about this field: it must have a potential energy that both supports inflation and ends it. We know it must have a shape that supports a sufficient amount of inflation. In its simplest form consistent with these requirements, it also makes predictions: namely, that the density perturbations will be adiabatic, Gaussian, and nearly scale invariant.
OK, now we are indeed talking about the mechanism, but are those predictions unique to the scalar potential approach, or are those behaviors endemic to a wide class of approaches? You say we can "effectively model" the inflation with a scalar potential, but if that is true, why are there so many different ways to do it, each with their own issues? How can we have a unifying principle here, if we cannot even identify which principle is the right one? I think the jury is still out on just how effective that approach can be judged, but those on the inside of the effort might disagree.
And from this approach, I can discover, by observations of the observable universe alone, whether the potential that drove inflation in our Hubble patch is operative elsewhere in the universe. It doesn't matter that I don't know how exactly the inflaton arises from supergravity or some other theory. The data, together a suitable application of Occam's razor, are sufficient.
Then by all means, do what can be done! But until it is done, how do we know what can, or cannot, be done? I never said it's a bad idea, I just said it is speculative as to whether or not it is really going to fulfill its promise. And there's nothing wrong with that, new theory making is speculative, that's just what it is-- but why sell it as something more?
And I must caveat this discussion by saying that I am not a proponent of eternal inflation or of multiverse theories per se; I have no vested interest in their veracity. But I think it is too constrictive to maintain your tact that unless it is strictly observed that it has no place in science. Many things that belong in mainstream science have not been strictly observed but only inferred or implied by the strict consistency of theories that have been supported by other observations.
That particular tack was specifically about the geometry of the universe beyond what we can infer from observations. I'd say it's already pretty clear, whether or not we ever detect any curvature, that the curvature is not going to be enough to constrain the geometry of the rest of the universe without wholesale extrapolation. On what basis can the shape of a nose be extrapolated to the shape of a head? The cosmological principle is not a principle of extrapolation or constraint beyond what we can observationally falsify, it is simply a modeling principle in the domain of what we can.

Edit: but to clarify, I don't see myself as in any position to pass judgment on inflation to people who do it, I'm just saying that a lot of rather grandiose claims get made about inflation but a lot of them seem to come with a rather large portion of faith. It behooves us to be realistic about what we have a right to expect from our theories, and what we might have to accept is more difficult than we'd like! None of this is in any way an attempt to discredit inflation as a useful research direction.

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The cosmological principle is not a principle of extrapolation or constraint beyond what we can observationally falsify, it is simply a modeling principle in the domain of what we can.

Strongly disagree.

Giordano Bruno was able to deduce the existence of exoplanets centuries before it became observationally possible to falsify them. He published his work in 1584, and it wasn't until the 1960's when it became possible even in principle to falsify their existence.

I don't see how multiverses are any different.

One other thing. This idea that observational falsification is the basis of science is quite new. Popper came up with it in the 1930's, and one problem that I have with discussions of the "scientific method" is that there is this idea that what is science and what isn't is self-evidently obvious and settled.

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Ken G
Gold Member
Giordano Bruno was able to deduce the existence of exoplanets centuries before it became observationally possible to falsify them. He published his work in 1584, and it wasn't until the 1960's when it became possible even in principle to falsify their existence.
The analogy does not hold. The only thing that makes exoplanets important is the simple fact that we can observationally verify their existence! That's exactly what we know we will not be able to do with some extended corner of the universe that has no observable consequences on what we can see, or worse, other universes altogether. If the cosmological principle worked well on the scale of what we see, but started to fail on scales an order of magnitude larger, I don't see how we would ever know that, constraints like that seem pretty much a pipe dream.
I don't see how multiverses are any different.
The difference is fundamental and crucial, it is what makes exoplanets science and multiverses not science (I argue). And it is straightforward: we can observe planets. Science is what we can observe. Yes, we are allowed to draw inferences, assume interactions, etc., but multiverses are not postulated because they interact, or because we can draw inferences about them, they exist simply to make us feel better about being in a seemingly very special universe, when rationalistic thinking about the "laws" of physics don't accommodate specialness very well. Bruno's speculations about planets had nothing to do with that motivation, he just realized the hugely important unifying principle of equating our Sun with other stars. It has only become science since we have been able to observe those planets.
One other thing. This idea that observational falsification is the basis of science is quite new. Popper came up with it in the 1930's, and one problem that I have with discussions of the "scientific method" is that there is this idea that what is science and what isn't is self-evidently obvious and settled.
I don't think it is accurate that a stress on observational falsification is all that new, it's actually incredibly hard to come up with anything that is new in philosophy! But Popper certainly popularized the idea. Anyway, I agree with your central point, that it is not at all obvious what "science" really is in the first place, but that's the whole reason why it's important to be skeptical that multiverse thinking is really science. What science is evolves constantly, and if one is not careful, one's science can evolve into something that is rather a large step backward, into realms where science becomes a way to feel good about what one knows, rather than a prescription for constantly requiring empirical demonstration in order to hold that one knows it.

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It's not important to me to be able to label inflation "ad hoc", I'm perfectly happy with "currently speculative details of how it works." I hope inflation works out simply, why wouldn't I. I'm just saying we should not kid ourselves that we have good reason to expect a scalar potential mechanism to turn out to be the correct description of the phenomenon of inflation.

We actually do. If you have a vector or tensor potential, then you'll end up with topological defects. What happens is that you have different parts of space go down vector potentials in different directions, so you'll end up with places where the vectors change direction suddenly, and those result in strong signals that we don't see in the CMB.

So whatever caused inflation was largely a scalar potential.

I'm saying it is appropriate to separate the phenomenon of inflation, which is simply the statement that the universe expanded by the factor X at epoch Y, from any physical theories or mechanisms that can actually accomplish that.

I'm not sure I see the point. One thing about astrophysics is that there are lots of examples in which we have a phenomenon with an unknown mechanism. We don't have a good mechanism for supernova, or accretion jets.

Things like reheating and so forth could be examples of the mechanism working, beyond just the phenomenon, but these are exactly the kinds of details that are still being thrashed out, and remain unclear as to whether or not they are going to work.

But the first thing is to establish that something exists. We don't understand the mechanism behind supernova, but we know supernova exist. We don't understand the mechanism behind inflation, but we know it happened.

Maybe you're right that if I knew better all the things that scalar potentials are doing for us, I'd be more inclined to see that approach to inflation as a unifying principle.

This is why I'm so harsh about LCDM and your efforts to get rid of mathematical baggage.

The big evidence for inflation is that if you assume that that there was massive expansion due to a scalar potential, you end up with a fluctuation spectrum. Because of quantum noise, some places have higher density, some places have lower density and this gets expanded by inflation. You can do detailed mathematical calculations about the density spectrum, and voila, it matches what we see when we look at WMAP.

If you try to get rid of this "mathematical baggage" for the sake of simplicity then all of this disappears. At this point inflation just becomes a fairy tale.

But it starts to sound a bit like string theory, which I am also assured is doing wonderful things for our understanding, except that it hasn't really delivered what it claimed it would.

Which is what happens when you get rid of the details. Just to use another analogy. We are *way* past the "earth is round" stage of cosmology. With LCDM, we can see the individual peaks and valleys of the universe. We can make very detailed calculations of the CMB background.

If you get rid of the "useless math baggage", then you also get rid of the ability to make complex and detailed predictions.

OK, now we are indeed talking about the mechanism, but are those predictions unique to the scalar potential approach, or are those behaviors endemic to a wide class of approaches? You say we can "effectively model" the inflation with a scalar potential, but if that is true, why are there so many different ways to do it, each with their own issues?

Because reality is complicated. There's also a tradeoff. One reason that we can use inflation for a lot of things is that it turns out that most of the predictions of inflation are not model dependent, but if the observations are model independent, then you have a plethora of models that fit the observations.

How can we have a unifying principle here, if we cannot even identify which principle is the right one?

Because for a lot of things, the details don't matter. With inflation you end up with two numbers which you then put into LCDM. How you got those two numbers, that doesn't matter.

And there's nothing wrong with that, new theory making is speculative, that's just what it is-- but why sell it as something more?

But it's not that speculative. You get CDM power spectrum out of it.

I'd say it's already pretty clear, whether or not we ever detect any curvature, that the curvature is not going to be enough to constrain the geometry of the rest of the universe without wholesale extrapolation. On what basis can the shape of a nose be extrapolated to the shape of a head?

Because CDM density perturbations can give you the limit of anisotropy, and can give you limits for how much the universe expanded during inflation. If you start with the premise that the fluctuations are due to quantum differences in density, you can calculate how much the universe expanded in order to give the current observations. You can also calculate the limits at which nearby bits could be different which gives you a radius at which you expect things to be isotropic.

What's happening is that you are taking a theory, stripping out the important bits as "useless mathematical baggage" and then complaining that the theory makes no real predictions.

The cosmological principle is not a principle of extrapolation or constraint beyond what we can observationally falsify, it is simply a modeling principle in the domain of what we can.

Exoplanets.

The analogy does not hold. The only thing that makes exoplanets important is the simple fact that we can observationally verify their existence!

Yes with the technology that we have in 2012. Not in 1584, and it wasn't until the 1960's that we had anything close to the technology necessary to verify exoplanets.

That's exactly what we know we will not be able to do with some extended corner of the universe that has no observable consequences on what we can see, or worse, other universes altogether.

Who is "we"?

Off the top of my head, I can't think of how to observationally verify multiverse scenarios, but if you were to ask Giordano Bruno in 1584 how he intends to verify the existence of exoplanets, he couldn't tell you either.

Even "build a big telescope" wouldn't work. The optical telescope hadn't been invented until 1600.

If the cosmological principle worked well on the scale of what we see, but started to fail on scales an order of magnitude larger, I don't see how we would ever know that

Stare at the problem for a few hundred years before giving up.

The difference is fundamental and crucial, it is what makes exoplanets science and multiverses not science (I argue)

We weren't able to observe exoplanets until the 1990's. Now if you are making the statement that we will *never* be able to observe multiverses, then I think that's highly, highly premature.

A lot of the research on the idea of multiverses is to figure out what the impact on CMB background would be. We can actually exclude some scenarios based on what we know.

Bruno's speculations about planets had nothing to do with that motivation, he just realized the hugely important unifying principle of equating our Sun with other stars. It has only become science since we have been able to observe those planets.

So exoplanets were "unscientific" until 1990? That seems to me absurd. Also, we'd never even begin to observe exoplanets until we tried, and we couldn't try until we had a theory that described what we were looking for.

I don't think it is accurate that a stress on observational falsification is all that new, it's actually incredibly hard to come up with anything that is new in philosophy! But Popper certainly popularized the idea.

He invented it. There are some obvious problems with Popper's ideas.

Ken G
Gold Member
Yes with the technology that we have in 2012. Not in 1584, and it wasn't until the 1960's that we had anything close to the technology necessary to verify exoplanets.
I would say that what emerges here is an important distinction between what is science, and what inspires science but isn't itself science. Bruno was not doing science when he speculated the existence of planets, because he was not offering any tests of his idea. But it was clear enough that the suggestion could be turned into science as soon as we had the technology to see that far or that well. Similarly, Edgar Allen Poe was not doing science when (in 1848!) he speculated that the universe was expanding, but he might have inspired the science of cosmology (it is unknown if Friedmann read "Eureka", but it is known he was a Poe enthusiast). Immanual Kant wasn't doing science when he speculated the existence of "island universes" of stars, but he might have helped inspire the scientific pursuit of the study of galaxies. The point is, we can speculate anything we like, whether it be ESP or angels or galaxies, and we can be proven right or wrong, but what makes something science is the act of trying to support or falsify some idea with observations. It's a fine line, but to me the guiding principle is whether we are letting nature answer the question, or if we are pushing our answer down nature's throat. I guess everyone has to make that choice for themselves, in regard to the multiverse speculation.
He invented it.
In looking into it, I have come to agree with you-- Popper really does seem to have arrived at his views, on the importance of falsifiability in the definition of science, entirely through his own experiences with certain theories of his day that were claiming to be science. I think he actually has quite a few extremely good points, and at risk of going further off topic, I'll offer up what I see as a brilliant quote from him, on the topic of the pitfalls of inductive logic when it is allowed to become particularly careless (from http://www.stephenjaygould.org/ctrl/popper_falsification.html), it's just such a gem, and is not completely unrelated to the question of whether the multiverse is science:

'The most characteristic element in this situation seemed to me the incessant stream of confirmations, of observations which "verified" the theories in question; and this point was constantly emphasize by their adherents. A Marxist could not open a newspaper without finding on every page confirming evidence for his interpretation of history; not only in the news, but also in its presentation — which revealed the class bias of the paper — and especially of course what the paper did not say. The Freudian analysts emphasized that their theories were constantly verified by their "clinical observations." As for Adler, I was much impressed by a personal experience. Once, in 1919, I reported to him a case which to me did not seem particularly Adlerian, but which he found no difficulty in analyzing in terms of his theory of inferiority feelings, Although he had not even seen the child. Slightly shocked, I asked him how he could be so sure. "Because of my thousandfold experience," he replied; whereupon I could not help saying: "And with this new case, I suppose, your experience has become thousand-and-one-fold." '

I would say that what emerges here is an important distinction between what is science, and what inspires science but isn't itself science. Bruno was not doing science when he speculated the existence of planets, because he was not offering any tests of his idea.

But then you've marked what most theorists do as "non-science." Theorists often do not come up with tests of their ideas, because that's for other people (maybe in several decades) to figure out.

One of the major predictions of general relativity was gravity waves, but Einstein didn't offer any tests for that idea. For that matter, I don't think that Einstein in his papers on special relativity offered *any* experimental tests for it.

The point is, we can speculate anything we like, whether it be ESP or angels or galaxies, and we can be proven right or wrong, but what makes something science is the act of trying to support or falsify some idea with observations.

*Trying*

There's no need that the scientist come up with a way of falsifying the idea *right now*.

Also, you can falsify an idea with theoretical constraints. If you come up with a theory of gravity, and it requires faster than light travel, you are going to have to do a lot of arguing to get that accepted.

As far as Popper's statements, I have problems with 7). The point about patching theories in order to fit observations is something that scientists do all the time. The "conversationist strategm" is something that's a good description of how science is done. You have a model. It doesn't work, you patch the model. Marxism-1919 is different from Marxism-1888, but electroweak theory-2012 is different from electroweak theory-1973. In order to get everything to work, we've had to tweak and retweak the big bang, but that hardly renders it less "scientific."

One thing that come in after Popper was the concept of "paradigms." Popper's world is very brittle, you find one thing wrong with your theory and then what?

The other thing is that it's very odd to say from the point of view of 2012 that Marxism or psychoanalysis are irrefutable. Most people would consider Marxism to have between refuted. Yes it's possible to get swept up by the crowd, but that happens with physics too (witness supersymmetry).

The other problem with Popper's ideas is that taken to the extreme, it makes it impossible to say anything meaningful about people or societies. In physics you *usually* don't have this problem. Most things in physics are not one time events and you can figure out what happens with repeated experiments. This isn't the case with societies, and it's also not the case with cosmology.

Here's problem with Popper's criteria. Quantum mechanics. QM creates only probabilistic predictions, and there is no observation or set of observations that could refute QM. If you observe anything, you could always just say that you were *very* unlucky.

bapowell
Here's problem with Popper's criteria. Quantum mechanics. QM creates only probabilistic predictions, and there is no observation or set of observations that could refute QM. If you observe anything, you could always just say that you were *very* unlucky.
I would argue that this is true of science in general. All measurements are uncertain, and so are all conclusions. The only difference with quantum mechanics is that the uncertainty is fundamental, but to experimental science, all that matters is that there be uncertainty.

Ken G
Gold Member
But then you've marked what most theorists do as "non-science." Theorists often do not come up with tests of their ideas, because that's for other people (maybe in several decades) to figure out.
So you are saying that Bruno, Kant, and Poe were astrophysical theorists? After all, not only did they theorize, they were also right. You don't see any "blind squirrel" phenomena there? After all, none of those three were basing their theories on a single shred of observational evidence.
One of the major predictions of general relativity was gravity waves, but Einstein didn't offer any tests for that idea. For that matter, I don't think that Einstein in his papers on special relativity offered *any* experimental tests for it.
At no point did I say that a theorist had to offer experimental tests, I said a theory had to offer experimental tests. I'm sure you see the difference.
Also, you can falsify an idea with theoretical constraints. If you come up with a theory of gravity, and it requires faster than light travel, you are going to have to do a lot of arguing to get that accepted.
Just look at your words! Now theories should be accepted or refuted entirely based on the "amount of arguing" they require? There is always going to be pedagogical issues and a search for consensus, all of which is basically rhetoric, but sadly I think we are indeed seeing a lot these days of pure mathematical rhetoric. (Look at Hawking radiation, for example-- has there ever been an example of a theory so widely accepted as representing a real phenomenon on grounds that involve extrapolation of a theory into wholly untested domains, and with so little likelihood of ever receiving experimental demonstration? Popper would have cringed, I suspect.) Theories should be accepted or refuted based on only one thing: experimental results. But these days we are seeing way too much of the mathematical equivalent of rhetoric, in place of the basic skepticism and demand for demonstration that should underpin science. It's not necessarily bad, as it's really all we have to go on right now, but it's too oversold, there just needs to be more "truth in advertising" about what is speculation and what has empirical support.
As far as Popper's statements, I have problems with 7). The point about patching theories in order to fit observations is something that scientists do all the time. The "conversationist strategm" is something that's a good description of how science is done. You have a model. It doesn't work, you patch the model. Marxism-1919 is different from Marxism-1888, but electroweak theory-2012 is different from electroweak theory-1973. In order to get everything to work, we've had to tweak and retweak the big bang, but that hardly renders it less "scientific."
I agree (7) is the most questionable, the rest are all pretty rock solid. I think what rescues (7) is what is meant by "ad hoc", albeit this is a difficult word to define clearly. It seems to me that Popper's sentiment here is that a theory that is in a state of "constant backpedalling" is probably a theory that is not worth having, whereas a theory that almost got it right but needed some fixes that did not deviate from the central stance of the theory (so was not "ad hoc") is still a good theory. What I think is missing from (7) is some clear way to "count the unifications" of a theory, such that if you need X patches in a theory that accomplishes Y unifications, this is still science if X < Y. He seems to be complaining more about when X=Y, effectively reducing Y to zero. I think that's the phenomenon he witnessed with some theories of his day that gained a lot of momentum but never really "delivered the goods." It's a cautionary tale we do well to keep an eye on today as well, I wager!

So I see Popper as having two fundamental beefs with theories that he did not consider good science:
1) theories that were so versatile they could explain anything, thereby explaining nothing because they achieved no fundamental unification of the unknowns, and
2) theories that required so many patches to respond to their failings that any unifications they originally promised ended up vanishing in all the patches.
I think those are two mighty good points to bear in mind.
Most things in physics are not one time events and you can figure out what happens with repeated experiments. This isn't the case with societies, and it's also not the case with cosmology.
It is definitely a dicey issue when using physics to do history, as cosmology does, for just this "unrepeatability" problem. But I think in cosmology, you can still apply Popper's basic scheme, you just have to generalize what "repeatability" means. You only get one "trial" to study, that's true, but you can study it in what seem like independent ways-- you can do observations of very different phenomena, that are all predicted by the theory, and in that sense each independent prediction allows "repeatability" in the efforts to falsify it. So probably the stress on "repeatibility" is not so crucial there, it is instead a kind of need for "independent confirmation", which is really what "repeatibility" mostly means anyway.

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Ken G
Gold Member
Here's problem with Popper's criteria. Quantum mechanics. QM creates only probabilistic predictions, and there is no observation or set of observations that could refute QM. If you observe anything, you could always just say that you were *very* unlucky.
It sounds like you are reading in a black-and-white character to "falsification" that was never intended by a mind as nuanced as Popper's. All he was saying is that confirmations don't mean a thing if there was not an honest chance of refutation. As a perfect example of this, I once heard a person doing experimental tests of special relativity saying that the only reason they were doing the tests was to show that SR was correct. Had they ever gotten a result that got that SR was wrong, they would have figured they did something wrong in the experiment. I had two reactions:
1) then what is the point of doing anything at all, and
2) it certainly doesn't sound like what they were doing could be called science.
I think Popper would have agreed. But I don't think there's any fundamental problem posed by statistical theories-- falsification simply means outcomes that have an "honest" chance of showing a different distribution than the predictions, in a way that you could not just twiddle some arbitrary parameter and recover agreement, and certainly where you would not simply conclude you did something wrong and not publish if you got disagreement. FTL neutrinos are a perfect example of the opposite-- the result was published, and even if the community is not "betting" on it, there is still a need to try and either reproduce the result, or pinpoint the cause of experimental error. Otherwise SR isn't science any more, it is dogma or delusion-- as I suspect Popper would say.

Haelfix
Theories should be accepted or refuted based on only one thing: experimental results. But these days we are seeing way too much of the mathematical equivalent of rhetoric, in place of the basic skepticism and demand for demonstration that should underpin science.

Sorry, but almost every working scientist will disagree with you here. Partially its b/c people have been fed Popper a little too much. In practise, there are often certain things that are simply not testable, not even in principle.

Even better. Sometimes there are things that are testable, but you just don't have to test b/c you know that it won't work.

For instance, if you told me that you have placed an apple on the surface of the moon, I insist that it would be irrational for me to hop into a NASA rocket to actually falsify the claim.

Yet another thought experiment. Suppose I was to tell you that you had a dollar in coins, that were split in some way under three black jars. I shuffle them, move them around and you open Jar 1 revealing that it has one dollar in change. The point is, you don't have to open Jar 2 and Jar 3. You know that they are empty by elementary logic under the assumption that I haven't cheated in some way.

Something a little more sophisticated, but essentially the same occurs in elementary particle physics. Sometimes, you simply know (really truly) that an undiscovered particle has to be at a certain place. It is that way b/c the mathematics of previous discoveries imply and constrain such and such a thing to be where it is. So of course while an assumption might break down at one point or another (apples might suddenly fall upwards), you can sometimes really know something has to be a certain way.

Indeed, and here is the key. The most primary thing in all of science, is not experimental discovery, it is on the contrary the primacy of logic. The world is and must be logical. Without that starting assumption, no experiment ever conducted has any explanatory power whatsoever.

Ken G
Gold Member
Sorry, but almost every working scientist will disagree with you here.
Only if they misrepresent the argument as much as you are doing, as will become more clear.
For instance, if you told me that you have placed an apple on the surface of the moon, I insist that it would be irrational for me to hop into a NASA rocket to actually falsify the claim.
What does that have to do with the idea that mathematical rhetoric cannot substitute for observational falsification? The reason we doubt that there could be an apple on the Moon is that we have a vast array of observations that speak to the issue. We have observations of the surface of the Moon that indicate it is rocky and barren. We have a vast array of apple observations that say they grow on trees, which grow in soil, and need water and air. These all constitute experimental data that falsifies the hypothesis. I don't think Popper was saying we can't use our brains.

What's more, you are also arguing that Popper was saying we can't know that certain theories or hypotheses are bad. Nothing that Popper was talking about constitutes a requirement for calling a theory bad-- he was talking about requirements for calling a theory good.

Yet another thought experiment. Suppose I was to tell you that you had a dollar in coins, that were split in some way under three black jars. I shuffle them, move them around and you open Jar 1 revealing that it has one dollar in change. The point is, you don't have to open Jar 2 and Jar 3. You know that they are empty by elementary logic under the assumption that I haven't cheated in some way.
No one is saying you can't use logic, the issue is whether you are basing that logic on experimental evidence.
Something a little more sophisticated, but essentially the same occurs in elementary particle physics. Sometimes, you simply know (really truly) that an undiscovered particle has to be at a certain place. It is that way b/c the mathematics of previous discoveries imply and constrain such and such a thing to be where it is.
And what is "the mathematics of previous discoveries"? It is the conceptual unification of a body of experimental data. It is not a rationalistic argument that "the universe needs to be this way because it makes sense to us for it to be so." That's the difference, right there, between empirical evidence, and rhetoric. Either one can be logical, and mathematical, what distinguishes them is what underpins it. That seems to be to be what Popper was actually talking about, not being an idiot (Popper was fairly well educated as a physicist, after all).

So of course while an assumption might break down at one point or another (apples might suddenly fall upwards), you can sometimes really know something has to be a certain way.
I dropped that reasoning somewhere, on the surface it looks like "although you can't really know something, you can really know it." I'm reminded of Einstein's sage quote: "To the extent math refers to reality, we are not certain; to the extent we are certain, math does not refer to reality." But this is a secondary issue anyway-- no one is saying we shouldn't use mathematical logic as our primary tool for making connections between observations, the issue is whether it can stand entirely on its own, without such observational underpinning, and without making "risky" predictions that could actually be confronted with observation. Science must put a question to nature, not to our own heads, or it is back to the natural philosophy of yore.
Indeed, and here is the key. The most primary thing in all of science, is not experimental discovery, it is on the contrary the primacy of logic. The world is and must be logical. Without that starting assumption, no experiment ever conducted has any explanatory power whatsoever.
That is the mantra of rationalism, but I would argue it is exactly the "false turn" we have made all to many times in the past. When will we learn? Logic is a tool for science, it has no "primacy", any more than paint has "primacy" in art. Saying "the world must be logical" is much like the common erroneous framing of Occam's Razor, "the simplest explanation is most likely correct." I would argue that a far better way to frame both these ideas is, "physics seeks whatever logic we can find in the world", and "the goal is to find the simplest explanation that works." None of the important content of the ideas are lost when framed this way, and they actually become true.

if the universe is infinite and the 'big bang' didn't come from a singular point and happened everywhere at once. Wouldn't that nullify the whole big bang theory. And wouldn't we then detect certain areas in space moving toward us as others are moving away??